WASHINGTON — Top congressional Democrats demanded on Sunday that President Trump’s acting attorney general, Matthew Whitaker, recuse himself from overseeing the special counsel investigation, and vowed to use their newfound powers as the incoming House majority to block him from interfering with it.

The incoming chairman of the House Judiciary Committee, Representative Jerrold Nadler of New York, vowed to make Mr. Whitaker the panel’s first witness when the new Congress convenes in January — and subpoena him if necessary. The incoming chairman of the House Intelligence Committee, Representative Adam B. Schiff of California, said Democrats would investigate Mr. Whitaker, a Trump loyalist who has repeatedly and explicitly criticized the investigation into Russian interference in the 2016 presidential race.

“The questions we will ask him will be about his expressed hostility to the investigation, and how he can possibly supervise it when he’s expressed, when he’s come out and said the investigation is invalid,” Mr. Nadler said on CNN’s “State of the Union.”

And Senator Chuck Schumer of New York, the Democratic leader, warned that if Mr. Whitaker did not step aside, Democrats would attach legislation protecting the special counsel, Robert S. Mueller III, to a must-pass spending bill. But Mr. Schumer stopped short of saying that Democrats would shut down the government if such legislation did not pass.

“The appointment of Mr. Whitaker should concern every American,” Mr. Schumer said on“State of the Union,” adding that if Mr. Whitaker continues to oversee the inquiry, “he will create a constitutional crisis by inhibiting Mueller or firing Mueller.”

“So,” Mr. Schumer added, “Congress has to act.”

As they prepare to take control of the House, Democrats are trying to strike a delicate balance between pressing ahead with their legislative agenda and investigating an administration that has operated for two years without any real oversight from Congress. Representative Nancy Pelosi of California, the Democratic leader who hopes to become speaker, insisted on Sunday that Democrats do not intend to play politics with their investigatory powers.

“We are responsible. We are not scattershot,” Ms. Pelosi said on the CBS program “Face the Nation.” “We are not doing any investigation for a political purpose, but to seek the truth. So I think a word that you could describe about how Democrats will go forward in this regard is, we will be very strategic.”

But her colleagues made clear that they intend to move aggressively, not just in overseeing the Justice Department, but on a variety of fronts.

Representative Elijah E. Cummings of Maryland, who will become chairman of the House Oversight and Government Reform Committee, said he intended to look at whether Mr. Trump had violated the emoluments clause of the Constitution, which prohibits federal officials from receiving gifts, or emoluments, from foreign powers. Many Democrats believe that Mr. Trump is violating the clause by continuing to profit from his worldwide real estate dealings.

Mr. Cummings, speaking on ABC’s “This Week,” said that “there are probably many” violations by Mr. Trump. He also vowed to look into reports that Mr. Trump had blocked the federal government from moving the F.B.I. headquarters, which sits across Pennsylvania Avenue from his downtown Washington hotel, because doing so would have cleared the way for construction of a competing hotel.

“We’ve got to figure out when is he acting on behalf of the American people in a lot of his decisions or — or is he acting on his own behalf?” Mr. Cummings said. But he said he saw subpoenas as a last resort, and ducked a question about what he would do if the White House refused to comply with them.

“We will cross that bridge when we get to it,” he said.

House Democrats also plan to investigate whether Mr. Trump used what Mr. Schiff called “instruments of state power” to try to punish The Washington Post and CNN, whose journalists asked questions of the president that Mr. Trump did not like. The White House revoked the credentials of the CNN correspondent Jim Acosta last week after Mr. Acosta confronted Mr. Trump at a raucous news conference, and the president has warned that more journalists may lose their credentials.

Mr. Schiff, in an interview with the website Axios, said Congress should examine whether Mr. Trump attempted to block AT&T’s merger with Time Warner as “an effort to punish CNN.” He also accused Mr. Trump of “secretly meeting” with the postmaster general to prod her into “raising postal rates on Amazon,” whose chief executive and founder, Jeff Bezos, owns The Washington Post.

“This appears to be an effort by the president to use the instruments of state power to punish Jeff Bezos and The Washington Post,” Mr. Schiff said.

But perhaps nothing is as high on Democrats’ agenda as protecting the Mueller investigation. Mr. Whitaker has stirred deep concerns among Democrats since Mr. Trump, on the heels of the Republicans’ loss of the House last week, named him acting attorney general after firing Jeff Sessions, who had long endured Mr. Trump’s wrath over the Russia inquiry. Among other comments, Mr. Whitaker had once declared that there was “no collusion” between the Trump campaign and Russia — a remark that prompted Democrats to say he had prejudged the inquiry’s conclusion.

Mr. Whitaker’s appointment went outside the usual Justice Department plan of succession. Ordinarily, Rod J. Rosenstein, who had protected the Russia inquiry as deputy attorney general, would have ascended to the top job. Unlike Mr. Rosenstein, Mr. Whitaker, who was Mr. Sessions’s chief of staff, lacks Senate confirmation. Democrats say the appointment is unconstitutional.

“If he doesn’t recuse himself, if he has any involvement whatsoever in this Russia probe, we are going to find out,” Mr. Schiff warned on NBC’s “Meet the Press,” adding, “Mr. Whitaker needs to understand that he will be called to answer, and any role that he plays will be exposed to the public.”

Mr. Schumer said he and Ms. Pelosi, along with other Democrats, were sending a letter to the top ethics officer at the Justice Department, asking whether he had advised Mr. Whitaker to withdraw. The department’s ethics official had advised Mr. Sessions to withdraw from overseeing the investigation shortly after he took office last year, given his role in the Trump campaign, and Mr. Trump never forgave Mr. Sessions for stepping aside.

Correction:

Earlier versions of this article incorrectly referred to the postmaster general. She is Megan J. Brennan.

A version of this article appears in print on , on Page A16 of the New York edition with the headline: House Democrats Vow to Bar Whitaker From Interfering in Russia Inquiry. Order Reprints | Today’s Paper | Subscribe